The mixed problem for the Lamé system in a class of Lipschitz domains

We consider the mixed problem for the Lamé system{Lu=0in Ω,u|D=fDon D,∂u∂ρ=fNon N,(∇u)∗∈Lp(∂Ω) in the class of bounded Lipschitz creased domains. Here D and N partition ∂Ω   and ∂/∂ρ∂/∂ρ stands for the traction operator. We suppose the Dirichlet data fDfD has one derivative in Lp(D)Lp(D) and the traction data fNfN is in Lp(N)Lp(N). For p   in a small interval containing 2, we find a unique solution to the mixed problem subject to the condition that the non-tangential maximal function of the gradient of the solution is in Lp(∂Ω)Lp(∂Ω).